Vaccines are delicate biological substances that gradually become inactive over time and must be kept under a recommended temperature range of 2–8 °C for both short and long-term storage. Exposure to heat or freezing temperatures can highly affect the immunological properties of these vaccines and make them completely ineffective. Research shows that vaccine exposure to temperatures outside the recommended range is 33% in developed countries and 37.1% in developing countries. In practice, vaccines are stored in refrigerators, while thermometers and data loggers are used to record and monitor temperatures. However, traditional systems are unreliable due to lack of battery backup, human error, periodic logging of temperatures, etc. Therefore, an effective and reliable vaccine tracking and monitoring system is urgently needed. This paper proposes a blockchain-based, smart contract enabled solution that ensures an enhanced level of security, transparency, and traceability of stored vaccines in a health clinic, and enables the complete history of every vaccine to be checked from the day the vaccine is received by the health clinic to the date it is used or expires. We also formally analyze the resiliency of the proposed system against several attacks and compare the system with existing blockchain and non-blockchain-based solutions.